Mao Chengsi, Yi Changhao, Zhu Huangjun
Fudan University, Fudan University, State Key Laboratory of Surface Physics, Department of Physics, and Center for Field Theory and Particle Physics, Shanghai 200433, China; Institute for Nanoelectronic Devices and Quantum Computing, Shanghai 200433, China and Shanghai Research Center for Quantum Sciences, Shanghai 201315, China.
Phys Rev Lett. 2025 Apr 25;134(16):160801. doi: 10.1103/PhysRevLett.134.160801.
Shadow estimation is a sample-efficient protocol for learning the properties of a quantum system using randomized measurements, but the current understanding of qudit shadow estimation is quite limited compared with the qubit setting. Here, we clarify the sample complexity of qudit shadow estimation based on the Clifford group, where the local dimension d is an odd prime. Notably, we show that the overhead of qudit shadow estimation over the qubit counterpart is only O(d), which is independent of the qudit number n, although the set of stabilizer states may deviate exponentially from a 3-design with respect to the third moment operator. Furthermore, by adding one layer of magic gates, we propose a simple circuit that can significantly boost the efficiency. Actually, a single magic gate can already eliminate the O(d) overhead in qudit shadow estimation and bridge the gap from the qubit setting.
阴影估计是一种使用随机测量来学习量子系统性质的样本高效协议，但与量子比特情形相比，目前对量子位阴影估计的理解相当有限。在这里，我们阐明了基于克利福德群的量子位阴影估计的样本复杂度，其中局部维度(d)是一个奇质数。值得注意的是，我们表明，与量子比特对应物相比，量子位阴影估计的开销仅为(O(d))，这与量子位数(n)无关，尽管稳定器状态集相对于第三矩算子可能与3 - 设计呈指数偏差。此外，通过添加一层魔术门，我们提出了一个可以显著提高效率的简单电路。实际上，单个魔术门已经可以消除量子位阴影估计中的(O(d))开销，并弥合与量子比特情形的差距。
